This paper reports on a major step in the development
of the extensive programme of exploration of the dynamics of
\(Sp(2N)\)  gauge theories on the lattice [1]}, [2]}, [3]}, [4]}, [5]}, [6]}.
We considered the lattice field theory with gauge group \(Sp(4)\) , with matter field content
consisting of two Wilson-Dirac fermions transforming in the fundamental representation,
together with three transforming in the 2-index antisymmetric representation.
Due to the odd number of fermions, the contribution of matter fields to the
non-perturbative dynamics is included by implementing a combination of
HMC and RHMC algorithms, both of which are supported by the HiRep code [7]},
which we adapted to the treatment of \(Sp(2N)\)  groups and to the
simultaneous handling of fermions in multiple representations.
The continuum limit is the minimal theory—amenable to lattice numerical studies [8]}—that
provides a UV completion for
the strongly-coupled sector of extensions of the standard model which combine
composite Higgs and partial top compositeness.
